NOTE: Items with spaces between them show the order in which to buy the components if you do not have the required amount. You may sell Heart of Gold in order to make space for Phantom Dancer or Infinity Edge.

1. Combo Puncturing Taunt along with Exhaust for serious -ARMOR to foes.
2. Combo Puncturing Taunt along with Defensive Curl to force foes to take damage from curl.
3. Use Defensive Curl for a damage increase and mitigation during battles.
4. Use Tremors to farm creep waves whenever possible. Do NOT save it for a tower.
5. Use Power Ball to initiate, chase, or as an escape mechanism.
6. Stay in the middle of team fights to abuse Tremors and Aegis of the Legion.

The following was tested in a practice game. There is no guarantee on the functionality of this build. I am not responsible for any damages caused to accounts or significant ELO drops of those who use this build. If there are signs of raging teammates, Rammus buff threads, or Riot representatives accusing you of griefing, please consult a psychologist, as these may be signs of failure.

Just getting infinity edge isn't going to increase your damage output that much, if your game even lasts that long, he'll still be hitting at a snail's pace. At that point in the game, a frozen heart would probably increase your utility and damage by a lot more.

Problems I see:
Attack Speed. He's not that fast. (Obviously if PD is taken, this is reduced and damage is switched for this.)
You're Rammus (Your team is losing out on some amazing tank potential if you do this. On the other hand, if your team already has too many tanks...well, it could work as an alternative DPSr. Also, people will laugh. Like those guys.)

Edit: Honestly, this might work. Kind of like my "WTFDPS Chog" build. But, unless there's really no other option you would be best sticking with your normal build. I see potential for a Rammus AP build, with RoA stacking for turret killing/ 1:1 PowerBall, but I think a Carrammus would be a bit too much given up for a bit too little in carry potential.
Bad Mana (Always a Rammus Problem. This build does nothing to fix it, like a Frozen Heart Rammus does.)
Weakened Pushing Power (Frozen Heart Rammus has his cooldowns up 25% quicker, which means a higher chance it'll be up when you're pushing towers.)

As a rammus main, this item build is redundant.
Must have major mana issues (no powerballing around the map), and lategame he wont be near invincible vs melee, pushing base towers etc.

Spending any gold in physical damage gear isn't worth it, he's super slow, and late game (unless you're ganking squishies) he's mostly best as a giant sponge and initiating stuff for the team, while helping your team win the game.